## The first three books of Euclid's Elements of geometry, with theorems and problems, by T. Tate |

### Inni boken

Side 6

XII , “ If a straight line meets two straight lines , so as to make the two interior angles on the same

XII , “ If a straight line meets two straight lines , so as to make the two interior angles on the same

**side**of it ... to AB ; and because the point B is the centre of the circle ACE ,**BC**is equal to BA : But it has been proved that ca ... Side 9

angles contained by those

angles contained by those

**sides**equal to one another , their bases shall likewise be equal , and the triangles be equal , and their other ... and the base**bc**is common to the two angles BFC , CGB ; wherefore the triangles are equal ( 1. Side 10

Let ABC be a triangle having the angle ABC equal to the angle ACB ; the

Let ABC be a triangle having the angle ABC equal to the angle ACB ; the

**side**AB is also equal to the**side**AC . ... because in the triangles DBC , ACB , DB is equal to AC , and**BC**common to both , the two**sides**DB ,**BC**are equal to the ... Side 11

Let ABC , DEF be two triangles having the two

Let ABC , DEF be two triangles having the two

**sides**AB , AC , equal to the two**sides**, DE , DF , each to each , viz . AB to DE , and AC to DF ; and also the base A**BC**equal to the base EF . The angle BAC is equal to the angle EDF . Side 12

that have their

that have their

**sides**which are terminated in one extremity of the base equal to one another , and likewise their**sides**terminated in the other extremity : But this is impossible ( 1. 7. ) ; therefore , if the base**Bc**'coincides with the ...### Hva folk mener - Skriv en omtale

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### Andre utgaver - Vis alle

The first three books of Euclid's Elements of geometry, with theorems and ... Euclides Uten tilgangsbegrensning - 1851 |

The First Three Books of Euclid's Elements of Geometry from the Text of Dr ... Euclid,Thomas Tate Ingen forhåndsvisning tilgjengelig - 2014 |

The First Three Books of Euclid's Elements of Geometry from the Text of Dr ... Euclid,Thomas Tate Ingen forhåndsvisning tilgjengelig - 2014 |

### Vanlige uttrykk og setninger

ABCD angle ABC angle ACB angle BAC angle equal base BC BC is equal bisect centre circle ABC circumference coincide common construct demonstrated describe diameter divided double draw equal angles equal to FB equilateral exterior angle extremity figure fore four given point given straight line gnomon greater impossible interior isosceles triangle join less Let ABC likewise line be drawn lines AC meet opposite angles opposite sides parallel parallelogram pass perpendicular PROB produced PROP Q.E.D. PROP rectangle contained remaining angle right angles segment semicircle shown sides squares of AC straight line A B Take taken THEOR third touch touches the circle triangle ABC twice the rectangle vertex wherefore whole

### Populære avsnitt

Side 6 - If a straight line meets two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...

Side 5 - Let it be granted that a straight line may be drawn from any one point to any other point.

Side 20 - If two triangles have two sides of the one equal to two sides of the...

Side 30 - Parallelograms upon equal bases, and between the same parallels, are equal to one another.

Side 17 - Any two angles of a triangle are together less than two right angles. Let ABC be any triangle ; any two of its angles together are less than two right angles.

Side 84 - IF from a point without a circle there be drawn two straight lines, one of which cuts the circle, and the other meets it; if the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, be equal to the square of the line which meets it, the line which meets it shall touch the circle.

Side 82 - If from any point without a circle two straight lines be drawn, one of -which cuts the circle, and the other touches it; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.

Side 11 - UPON the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extremity.

Side 19 - To make a triangle of which the sides shall be equal to three given straight lines, but any two whatever of these must be greater than the third, (i.

Side 7 - From the greater of two given straight lines to cut off a part equal to the less. Let AB and C be the two given straight lines, whereof AB is the greater.